The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil

DOI10.1016/0024-3795(76)90021-5zbMath0386.15011OpenAlexW1969513875MaRDI QIDQ1249628

Robert C. Thompson

Publication date: 1976

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(76)90021-5

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21)

Related Items

Convex Sets of Hermitian Matrices with Constant Inertia, Balanced Truncation Model Reduction for 3D Linear Magneto-Quasistatic Field Problems, Simultaneous congruence of convex compact sets of Hermitian matrices with constant rank, A new look at pencils of matrix valued functions, Minimal symmetric factorizations of symmetric real and complex rational matrix functions, A matricial boundary value problem which appears in the transport theory, A canonical form for self-adjoint pencils in Hilbert space, Spectral factorization via Hermitian pencils, Lur'e equations and even matrix pencils, Matrix Pencils with Coefficients that have Positive Semidefinite Hermitian Parts, Spectral characterization and enforcement of negative imaginariness for descriptor systems, On selfadjoint matrix polynomials, Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils, Condensed Forms for Linear Port-Hamiltonian Descriptor Systems, Stable real invariant semidefinite subspaces and stable factorizations of symmetric rational matrix functions, Unnamed Item, Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint, On doubly structured matrices and pencils that arise in linear response theory., A variational principle for eigenvalues of pencils of Hermitian matrices, Canonical forms for Hamiltonian and symplectic matrices and pencils, Congruence and \(A^{-1}A^*\), Self-adjoint differential-algebraic equations, A structure‐preserving doubling algorithm for Lur'e equations, The Algebraic Riccati Equation without Complete Controllability, Standard CR manifolds of codimension 2, Classes of normal matrices in indefinite inner products, A generalization of Sylvester's law of inertia, Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems, On the distance to singularity via low rank perturbations, Semidefinite perturbations of analytic Hermitian matrix functions, On nonnegative invariant subspaces in indefinite scalar product spaces^†, Implicit QR algorithms for palindromic and even eigenvalue problems, Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems, Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence, Linear-quadratic Gaussian balancing for model reduction of differential-algebraic systems, Hermitian polynomial matrices, isometries and inertial signs, Anti-triangular and anti-\(m\)-Hessenberg forms for Hermitian matrices and pencils, The inertia of a Hermitian pencil, Matrix pencils with the numerical range equal to the whole complex plane, Pencils of complex and real symmetric and skew matrices, Spectral variation under congruence for a nonsingular matrix with 0 on the boundary of its field of values, Canonical form of para-Hermitian pencils, generalized spectral factorization, and optimal control over frequency region

Cites Work

• Unnamed Item
• Unnamed Item
• Principal submatrices. VIII: Principal sections of a pair of forms
• On the Canonical Form of a Non-Singular Pencil of Hermitian Matrices
• On the Equivalence of Pencils of Hermitian Forms
• The Equivalence of Non-Singular Pencils of Hermitian Matrices in an Arbitrary Field
• Sur la réduction canonique des couples de matrices
• On the Theory of Automorphic Functions of a Matrix Variable, II-The Classification of Hypercircles Under the Symplectic Group